I fixed up the inserts today. Each one was only held in place with one dollop of glue in one spot. No wonder they lifted or sunk!!
I ended up taking every single one of them out just to be thorough. I didn't need to use any heat to remove them either. The ones that had been under the mylar already had a healthy dose of isopropyl alcohol when I was removing that which I assume helped loosen the glue, but even the other ones higher up in the playfield, all I did was spray them with some isopropyl then give it some persuasion from behind with a socket tool.
I sanded the plain ones (these were also the ones that were sunken the most). I used wet dry sand paper on them of 400, then 600 then 1,200. They came up noticeably different after that being done (you can see the bottom 3 I have done in the following pic as a comparison). The ones with writing on I just polished up with Novus 2 & 3.
Here's a pic of the main ones that were sunken badly reinstalled. Obviously when I do my playfield touchups I will go around and do the black circles around all the inserts again. I did notice some of the other ones with writing on were ever so slightly concave, but trying to get them flat would have meant sanding off the lettering. I guess if I do go ahead and put some type of clear coat on the playfield when I finish then this shouldn't be an issue.
I also had a package arrive during the week: